| Issue |
ESAIM: M2AN
Volume 59, Number 6, November-December 2025
|
|
|---|---|---|
| Page(s) | 3131 - 3157 | |
| DOI | https://doi.org/10.1051/m2an/2025083 | |
| Published online | 01 December 2025 | |
A convergent time scheme for a chemotaxis-fluids model with potential consumption
1
Departamento de Matemática, Instituto de Matemática, Estatística e Computaç˜ao Científica, Universidade Estadual de Campinas, Campinas, Brazil
2
EDAN and IMUS, Universidad de Sevilla, Sevilla, Spain
* Corresponding author: guillen@us.es
Received:
18
June
2025
Accepted:
29
September
2025
The present work deals with a Keller–Segel–Navier–Stokes system with potential consumption, under homogeneous Neumann boundary conditions for cell density and chemical signal, and Dirichlet type for the velocity field, over a bounded three-dimensional domain. The paper aims to develop a time discretization scheme converging to weak solutions of the system, which are uniformly bounded at infinite time. While global existence results are already known for simplified cases, either in absence of fluid flow or for linear consumption, the existence of global weak solutions for the fully coupled system with potential consumption has remained as an open problem.
Mathematics Subject Classification: 35K50 / 35K55 / 35Q30 / 65M12 / 76D05 / 92C17
Key words: Chemotaxis / Navier–Stokes equations / time discrete scheme / energy law / convergence / weak solutions
© The authors. Published by EDP Sciences, SMAI 2025
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